Honestly, I'm always amazed at the obsession with potty training....kids aren't dumb, they know exactly what they are supposed to do when it comes to going to the bathroom. Its a whole lot of steps to learn, a whole lot of emotional maturity involved, and a big step to becoming an independent child and leaving babyhood behind. Its no wonder some children decide that having the security of diapers means a lot to them and will resist 'training' until they are more emotionally mature.
Potty training is extremely fast if you have a child who is ready. For us, it was less than a day, but was entirely initiated by my daughter who announced 'no more diapers'. From that day out, no accidents, no diapers and she was ready for nighttime training within a week. Again, no accidents. I never pushed her and since I had a second baby to deal with, tried to put her off as much as possible since diapers are easier.
Remember, eliminating, like eating is entirely controlled by your child. Its not an area where you want to get into a power struggle. They will always win. Also, in my book, potty training is where the kids 'goes' when they need to, its not parent training where the kid is in underpants but you're the one dragging them to the toilet every hour coaxing them to go so they don't soil their pants.
As far as the three day program floating around on the internet, its a very harsh program designed for training toddlers at 22 months old. I'm not into berating my toddler for doing something natural like going to the bathroom. To each his own though.